Compactness of probability measures and the uniform convergence of certain stochastic series

V. V. Buldygin

Kiev State University

Abstract: We give the conditions which ensure the compactness of the probability measures $\mu_n$, $n\geqslant1$, generated by Gaussian processes the realizations of which are continuous with unit probability in $[0, 1]$. We also give the conditions for the uniform convergence of stochastic series of the form $\sum_{k=1}^\infty\xi_k(t)$, where the $\xi_k(t)$ are independent Gaussian processes the realizations of which are continuous with unit probability in $[0, 1]$.

UDC: 519.2

Received: 16.03.1971

 English version: Mathematical Notes, 1972, 12:4, 699–704

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